Abstract
A numerical method applicable to inviscid, compressible, two-dimensional, or axisymmetrical fluid flows is presented. It can be used to solve problems involving subsonic and transonic, as well as supersonic, flow regions. In this method, the streamlines and the equipotential lines are used as the orthogonal natural coordinates. These coordinates are approximated piecewise by small segments of circular arcs. In conjunction with a geometrical theorem concerning circular arcs, the gas dynamics equations in finite-difference form are integrated numerically. The flowfields may be constructed to a high degree of accuracy with a small number of steps. The boundary conditions are satisfied by an iteration procedure that converges rapidly. For examples, the flow behind a conical shock and the flow in a transonic hyperbolic nozzle are solved. The results are in good agreement with known solutions.
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